Alexander L. Velikovich

Richtmyer–Meshkov instability growth: experiment, simulation and theory

Richtmyer–Meshkov instability is investigated for negative Atwood number and two-dimensional sinusoidal perturbations by comparing experiments, numerical simulations and analytic theories. The experiments were conducted on the NOVA laser with strong radiatively driven shocks with Mach numbers greater than 10. Three different hydrodynamics codes (RAGE, PROMETHEUS and FronTier) reproduce the amplitude evolution and the gross features in the experiment while the fine-scale features differ in the different numerical techniques. Linearized theories correctly calculate the growth rates at small amplitude and early time, but fail at large amplitude and late time. A nonlinear theory using asymptotic matching between the linear theory and a potential flow model shows much better agreement with the late-time and large-amplitude growth rates found in the experiments and simulations. We vary the incident shock strength and initial perturbation amplitude to study the behaviour of the simulations and theory and to study the effects of compression and nonlinearity.

Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave

An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a ‘‘stand‐alone’’ rarefaction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration o...

Saturation of perturbation growth in ablatively driven planar laser targets

Saturation of the mass variation growth during the shock transit time, theoretically predicted for the surface roughness case by Ishizaki and Nishihara [Phys. Rev. Lett. 78, 1920 (1997)] and for the laser imprint case by Taylor et al. [Phys. Rev. Lett. 79, 1861 (1997)], is studied analytically and numerically. The saturation is demonstrated to be essentially the same effect in both cases, caused by the stabilizing action of mass ablation. Scalings of saturation time and saturation level for the two cases are related. For lower-density foam targets, the peak level of mass variation is proportional approximately to ρ01/2 and exactly to ρ0 for the cases of laser imprint and surface roughness, respectively.

Stability and radiative performance of structured Z‐pinch loads imploded on high‐current pulsed power generators

The stability and radiative performance of structured Z‐pinch plasma loads heated by high‐current (≳20 MA) pulsed power generators are investigated. A limited mapping of parameter space is made for the regions of stability for loads configured as thin shells, uniform fills, and multiple shells. Although large diameter thin shell loads are shown to be the most efficient radiators of K‐shell x rays, they are susceptible to disruption by the Rayleigh–Taylor instability. Large diameter uniform fill loads are shown to be more stable and very good radiators.

Reduction of Early-Time Perturbation Growth in Ablatively Driven Laser Targets Using Tailored Density Profiles

The effects of tailoring the density profile in a laser target in order to decrease imprinting of mass perturbations due to the long-wavelength modes are investigated analytically and numerically. Inverting the acceleration of the ablation front during the shock transit time could reduce the early-time mass perturbation amplitudes developed in the target after the shock transit. This principle was first suggested for mitigating the Rayleigh–Taylor (RT) instability of imploding Z-pinches [Velikovich et al., Phys. Rev. Lett. 77, 853 (1996); Phys. Plasmas 5, 3377 (1998)]. As the shock wave slows down propagating into higher density layers, the effective gravity near the ablation front has the same direction as the density gradient. This makes the mass perturbations near it oscillate at a higher frequency and at a lower amplitude than they normally would due to the “rocket effect” caused by mass ablation [Sanz, Phys. Rev. Lett. 73, 2700 (1994); Piriz et al., Phys. Plasmas 4, 1117 (1997)]. So, tailoring densit...

Stabilized radiative Z-pinch loads with tailored density profiles

Mitigation of the Rayleigh–Taylor (RT) instability of Z-pinch loads imploded from large initial radii through tailoring initial load density profiles in radial and axial directions is studied numerically. These methods could be helpful for a variety of applications of high-power Z-pinches, from producing large amounts of K-shell radiation to imploding inertial confinement fusion pellets. Radial density tailoring is demonstrated to delay the onset of the RT instability development at the expense of reducing the energy available for conversion into radiation. Axial density tailoring can fully stabilize acceleration of a fraction of the initial load mass. For a better tradeoff between stability and radiative performance of the loads, the density profiles could be tailored in two dimensions, combining the advantages of both methods. Post-processing of the radiation-magnetohydrodynamic simulation results demonstrates that an appreciable K-shell argon radiation power could be generated with a stabilized argon l...

Shock propagation in a low-density foam filled with fluid

It is found that when a planar shock is imparted to a system of a foam of low mean density filled with fluid (fiber density>ambient fluid density), an undercompressed quasisteady post-shock state is established. In this state, pressure and density are lower than the values predicted by Hugoniot relations for a uniform fluid with the same average fluid-foam density. It is shown that this undercompression phenomenon is due to residual correlations of fluctuations left after the saturation of the initially rapid mixing of fiber material with the background fluid. Generalized Hugoniot relations are derived for quasiplanar shocks in nonuniform systems, with foam as an example. The behavior of fluctuations in such systems is studied. Formulas for the level of fluctuations induced by a shock as it propagates through foam and for the relaxation time of the fluctuations, are derived.

Instability of a plane centered rarefaction wave

An analytic small‐amplitude theory of the instability of a plane centered rarefaction wave (which has recently been discovered numerically by Yang et al.) is presented. A finite‐difference (FCT) calculation is performed and compares well with the theory. The instability manifests itself as perturbation growth on the wave’s trailing edge. The asymptotic value approached by the perturbed velocity of the trailing edge is expressed as kδx0a0u∞(M,γ), where k is the perturbation wave number, δx0 is the constant perturbation amplitude of the leading edge, a0 is the sound speed in the unperturbed gas, and u∞(M,γ) is a dimensionless function that depends on the adiabatic exponent, γ, and the strength of the rarefaction wave, M, taken as the ratio of sound speeds behind and ahead of it. This function is essentially determined by the way the perturbed rarefaction wave is formed, e.g., by moving a corrugated piston from a gas‐filled space or by interaction of a plane shock wave with a rippled contact interface betwee...

Study of radiative plasma structures in laser driven ablating plasmas

The mechanism is analyzed that generates radiative plasma structures (RPS) [J. P. Dahlburg et al., J. Quant Spectros. Radiat. Transfer 54, 113 (1995)] in driven, ablating plasmas of subcritical density. A reduced set of radiation-hydrodynamics equations is derived which model the onset of RPS phenomenon.

Implosions, equilibria, and stability of rotating, radiating Z‐pinch plasmas

The effects of uniform rotation on the dynamics, equilibria and stability of cylindrically symmetric, radiating Z‐pinch plasmas are studied. Rotation changes the Bennett and Pease–Braginskii equilibria qualitatively, eliminating radiative collapse for both quasisteady and dynamic plasmas. In particular, a steady rotating plasma column can support any current above the Pease–Braginskii value, with Ohmic heating balanced by radiative losses. Stabilizing effect of rotation on the m=0 mode of Rayleigh–Taylor instability of a hollow plasma shell was found for long perturbation wavelengths.